I wondered why I wasn't able to get the mission earlier today. One thing I'm still a little unsure of though. Once the mission is complete, I'll get the Odyssey class. Since I'm already a VA, will I be able to keep it, or will it disappear from my inventory of ships for good?

Everything you need to know is in the Dev blogs. You can't get the mission yet because it isn't available until 10AM PST. The ship is free for everyone who does the mission meaning you keep it.